Mounted characters in infantry units

I'm wondering...

If a character on a mount joins a unit of rank and file infantry... is it possible to stop the unit from moving by casting "The Beast Cowers" upon it?

I'm sitting reading the rulebook looking for an answer, and it seems to boil down to the question "If a character (which counts as a unit containing one unit) joins a unit do the two units now combine to count as one unit, or are they still two units that are now under the effect of additional rules (eg being unable to be targeted directly or being restricted by the slowest model's M)?"

I'm kind of leaning towards "no", but it makes perfect real-world sense to be able to and I can't find the wording that says a character stops counting as a unit when it joins another unit.